Question

#What is the value of x?

`A. 4`

`B. 4sqrt3`

`C. 8`

`D. 8sqrt3`

Answer 1

`4sqrt(3) = x`, or B

Explanation:

In this one we know the angle and the hypotenuse, but we don't know the opposite side. So we need something to relate opposite to hypotenuse when given a certain angle.

`sin(theta) = "opposite"/"hypotenuse"` Works well here.

In this case we need to plug everything in as we see it. `theta` is 60 degrees, opposite is the opposite leg from the angle or `x`, and hypotenuse is the longest side to the triangle or 8 in this case.
So:

`sin(60) = x/8` Multiply 8 on both sides to isolate `x`
`color(red)(8)sin(60) = (x*color(red)(8))/8`
`8sin(60) = x` Now we just evaluate to get what x is equal to
`(8sqrt(3))/2 = x`
`4sqrt(3) = x`

So B is the answer